Uhm, we are all talking about doing this (investigating the monitor) while it's actually running right ? So yes, there's going to be 19,5 kV on the tube so........do not touch the cup (area). (And so there is no sense in first discharging the tube, and then turning it back on again so it's charged back up....).
I mean you should power up the game, then try to wiggle the connectors while it's running. I did that and got picture in a certain position of one connector and lost it when I left it alone again. Not fool proof, but worth a try.
Some things you will have to check when the monitor is running and yes there are all kinds of unhealthy voltages around but I guessed Spyridon is no noob who starts touching metal parts or pins of really big caps while it's running.
To wiggle the connectors try to touch the plastic case of the connector only.
My guess is you won't find much at the fuses as you have HV.
Read the WG6100 FAQ, that's the best walk-through you can get.
Basic things (even when wiggling doesn't indicate anything) check those connectors with a multimeter (WHILE THE MONITOR IS OFF !) with an Ohms measuring setting. Measure between the pin of the connector and the solder island of the part that the track runs to, NOT to the soldering island of the connector itself as this is probably good since the breaks develop around the soldering island.
Another basic thing is checking all the big transistors. Are the wires still OK, do the transistor holders still make good contact to the transistor pins etc.